A smooth wire has the form of the helix x = a cos θ, y = a sin θ, z = bθ, where…

A smooth wire has the form of the helix x = a cos θ, y = a sin θ, z = bθ, where θ is a real parameter, and a, b are positive constants. The wire is fixed with the axis Oz pointing vertically upwards. A particle P of mass m can slide freely on the wire. Taking θ as generalised coordinate, find the Hamiltonian and obtain Hamilton’s equations for this system.